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How do you use the limit definition to find the derivative of #y = cscx#?

1 Answer

Dec 2, 2016

The key parts are in the explanation section, below.

Explanation:

#(1/sin(x+h)-1/sinx)/h = (sinx-sin(x+h))/(hsin(x+h)sinx)#

# = (sinx-sinxcos h-cosxsin h)/(hsin(x+h)sinx)#

# = (sinx(1-cos h)/h - cosxsin h/h)*1/(sin(x+h)sinx)#

Taking the limit gets us

#(-cosx)/sin^2 x = -cscxcotx#

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